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Substitute Numbers for Letters in Complex Calculations (All Four Operations)

In this worksheet, students will replace letters with numbers and carry out questions using the four number operations, with some calculations in sets of brackets. They must give their final answers as numbers not letters.

Which of the calculations below shows the correct way to convert the letters into numbers?

10 x (3 +7)

10 + (3 + 7)

10 - (3 + 7)

10 ÷ (3 + 7)

If a = 8, b = 10, c = 4 and d = 12, what is a (d - c)?

Which of the calculations below shows the correct way to convert the letters into numbers?

8 x (12 + 4)

8 + (12 + 4)

8 x (12 - 4)

8 ÷ (12 - 4)

And now answer the question:

If a = 8, b = 10, c = 4 and d = 12, what is a (d - c)?

We know from the last question that a (d - c) converts to become 8 x (12 - 4).

Now complete the rest of the equation and write your answer as a number.

56

64

112

72

If A = 3, B = 12, C = 6 and D = 8, what is A (B - D)?

Which of the calculations below shows the correct way to convert the letters into numbers?

3 x (12 - 8)

3 + (12 + 8)

3 x (12 + 8)

3 ÷ (12 + 8)

And now let's solve the whole problem:

If A = 3, B = 12, C = 6 and D = 8, what is A (B - D)?

We know from the last question that A (B - D) converts to become 3 x (12 - 8).

Now complete the rest of the equation and write your answer as a number.

60

12

15

18

If a = 9, b = 15, c = 8 and d = 4, what is a (b - d)?

Which of the calculations below shows the correct way to convert the letters into numbers?

9 x (15 + 4)

9 + (15 - 4)

9 x (15 - 4)

9 ÷ (15 - 4)

Following on from the last question:

If a = 9, b = 15, c = 8 and d = 4, what is a (b - d)?

Work out the answer to the full equation and record your answer as a number.

99

81

72

63

If A = 8, B = 14, C = 7 and D = 3, what is A (B + D)?

Which of the calculations below shows the correct way to convert the letters into numbers?

8 x (14 - 3)

8 + (14 - 3)

8 x (14 + 3)

8 ÷ (14 - 3)

Following on from the last question:

If A = 8, B = 14, C = 7 and D = 3, what is A (B + D)?

Work out the answer to the full equation and record your answer as a number.

128

120

136

135

Insert brackets into the equation below to make it true.

ANSWERS

Question 1

If A = 10, B = 3 and C = 7, what is A (B + C)?

Which of the calculations below shows the correct way to convert the letters into numbers?

CORRECT ANSWER

10 x (3 +7)

EDDIE SAYS

The question tells us that A = 10, B = 3 and C = 7.
If we swap these numbers in for the letters, then A (B + C) becomes 7 (3 + 7).
When there is no symbol between a letter and the brackets, it means you should multiply the contents of the bracket by the number that comes before it. Or, in other words, you need to assume that a multiplication has been missed out.

ANSWERS

Question 2

If a = 8, b = 10, c = 4 and d = 12, what is a (d - c)?

Which of the calculations below shows the correct way to convert the letters into numbers?

CORRECT ANSWER

8 x (12 - 4)

EDDIE SAYS

The question tells us that a = 8, d = 12 and c = 4.
If we swap these numbers in for the letters, then a (d - c) becomes 8 (12 - 4).
When there is no symbol between a letter and the brackets, it means you should multiply the contents of the bracket by the number that comes before it. Or, in other words, you need to assume that a multiplication has been missed out.

ANSWERS

Question 3

And now answer the question:

If a = 8, b = 10, c = 4 and d = 12, what is a (d - c)?

We know from the last question that a (d - c) converts to become 8 x (12 - 4).

Now complete the rest of the equation and write your answer as a number.

CORRECT ANSWER

64

EDDIE SAYS

We know that we need to calculate the answer to 8 x (12 - 4).
Let's do the bracket first, 12 minus 4 gives us 8.
When we multiply 8 by 8, we reach the final answer of 64.
Were you able to complete the final step to reach the correct answer? Let's try another for some more practise...

ANSWERS

Question 4

If A = 3, B = 12, C = 6 and D = 8, what is A (B - D)?

Which of the calculations below shows the correct way to convert the letters into numbers?

CORRECT ANSWER

3 x (12 - 8)

EDDIE SAYS

The question tells us that A = 3, B = 12 and D = 8.
If we swap these numbers in for the letters, then A (B - D) becomes 3 (12 - 8).
Remember that a multiplication symbol is missing if there is nothing between a number or letter and a bracket.
So the final answer is 3 x (12 - 8).

ANSWERS

Question 5

And now let's solve the whole problem:

If A = 3, B = 12, C = 6 and D = 8, what is A (B - D)?

We know from the last question that A (B - D) converts to become 3 x (12 - 8).

Now complete the rest of the equation and write your answer as a number.

CORRECT ANSWER

12

EDDIE SAYS

We know that we must calculate the bracket first, which gives us an answer of 4.
When you multiply 3 by 4, we reach an answer of 12.
How are you doing with these tricky maths codes so far? Want some more practise?

ANSWERS

Question 6

If a = 9, b = 15, c = 8 and d = 4, what is a (b - d)?

Which of the calculations below shows the correct way to convert the letters into numbers?

CORRECT ANSWER

9 x (15 - 4)

EDDIE SAYS

The question tells us that a = 9, b = 15 and d = 4.
If we swap these numbers in for the letters, then a (b - d) becomes 9 (15 - 4).
If there is no symbol between a letter or number and a bracket, we need to assume that a x sign has been missed out.
So the correct answer is 9 x (15 - 8).

ANSWERS

Question 7

Following on from the last question:

If a = 9, b = 15, c = 8 and d = 4, what is a (b - d)?

Work out the answer to the full equation and record your answer as a number.

CORRECT ANSWER

99

EDDIE SAYS

We already know that we must calculate the bracket first, which gives us an answer of 11.
When you multiply 9 by 11, we reach an answer of 99.

ANSWERS

Question 8

If A = 8, B = 14, C = 7 and D = 3, what is A (B + D)?

Which of the calculations below shows the correct way to convert the letters into numbers?

CORRECT ANSWER

8 x (14 + 3)

EDDIE SAYS

The question tells us that A = 8, B = 14 and D = 3.
If we swap these numbers in for the letters, then A (B + D) becomes 8 (14 + 3).
We know that if we see a letter and a bracket next to each other without a symbol of operation (+, -, x, ÷), then we must assume that it is a multiplication.
Therefore, the correct answer is 8 x (14 - 7).

ANSWERS

Question 9

Following on from the last question:

If A = 8, B = 14, C = 7 and D = 3, what is A (B + D)?

Work out the answer to the full equation and record your answer as a number.

CORRECT ANSWER

136

EDDIE SAYS

We already know that we must calculate the bracket first, which gives us an answer of 17.
When you multiply 8 by 17, we reach an answer of 136.
We are really cracking those codes now! Just one question left...

ANSWERS

Question 10

Insert brackets into the equation below to make it true.

CORRECT ANSWER

8 x (21 - 6) = 120

EDDIE SAYS

The brackets would need to go around 21 - 6 to make the question true as this needs to be calculated first.
If this is done, then the sum becomes 8 x (15) which gives an answer of 120.
This equation can be further simplified by removing the multiplication sign to become 8 (21 - 6) = 120.
Great work maths coder!

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